I am confident that most veteran Republican strategists wish that QAnon never became a thing, much like they never wanted Trump to be their candidate in 2016. Now to be fair, I don't think anyone foresaw such a decentralized online conspiracy theory becoming such a powerful and enduring force (especially given how often "he" gives specific details of upcoming events that turn out to be plain wrong). I also believe that the GOP are now lying in the bed they've made, as both Trump and QAnon were only made possible as an unintended result of decades of GOP social strategy. I think though that the GOP's greatest issue with QAnon is not that the conspiracy theory has taken over large swaths of the conservative voter base who now follow it with fervor, but rather that they are unable to control it.
The modern GOP has always relied on stoking fear within the populace to foster a reliable voting base (note I am not saying that this applies to all GOP voters, but certainly a significant number). The specific targets of that fear have changed over time, but the strategy generally relies on demonizing an "other" who will supposedly come to destroy voters' way of life, and is often portrayed to be more powerful and influential than they truly are. See: Blacks, gays, communists (or whomever could be conveniently accused of being a communist during McCarthyism and the Red Scare), hippies/anti-war folk, Satanists, Muslims, transgender persons, Mexicans/Latin Americans, Antifa, BLM, etc.
Traditionally, that fear could be stoked strategically by way of coordinated (or at least semi-coordinated) messaging through specific avenues such as AM radio shock jocks, certain Evangelical preachers, Rush Limbaugh, the evening Fox News propaganda crew of Hannity/Ingraham/Carlson, etc. It was almost always framed in a US conservatives vs. the World way, but importantly always had the GOP as the defenders of the US conservative way of life.
Unfortunately for the GOP elite, the rise of Trump the populist has caused these sentiments of voter fear and anger to take on a life of their own. Trump came onto the scene as a fringe candidate, and wasted no time in capitalizing on this fear and anger with aggressive and inflammatory populist sentiments to get the nomination. Other than by stoking social and racial tensions (i.e. "telling it like it is", or more pessimistically "he hates the same people that I do"), how else could a New York City elitist who lives in a giant gold-plated tower in downtown Manhattan possibly make inroads as the anointed saviour of the US working class?
Trumpism has spawned a political orthodoxy among US conservatives unlike anything else I know of in US history. While this has always existed within politics to some extent (see for example the popularity of
RINO accusations in the past), never before has an huge segment of the voting population delegated their political opinions on a topic or person so directly to whatever Trump says or tweets. How many members of Trump's former senior advisors or members of his cabinet have gone from being considered courageous "swamp-drainers" to members of the "Deep State" or "never-Trumpers" just by virtue of being fired or publicly criticizing Trump?
QAnon and Trumpist orthodoxy are symbiotic, and I really don't think that one can be viewed without the other. Trumpism capitalizes on voter fear and anger. QAnon is popular as an explanation for Trump's "Deep State" rhetoric, and also provides explanations for many of the seemingly illogical statements and actions that Trump makes, and also reassures adherents that there is a deep master plan unfolding that can't be revealed just yet (soon though, promise). The nature of conspiracy theory and online grassroots QAnon communities on social media provide regular positive feedback loops for voters who have hitched their horse to the idea that right and wrong are a question of whatever Trump's position on the matter is.
I am confident that QAnon will remain popular for at least as long as Trump is in office, and will likely continue to inspire infrequent acts of lone-wolf political violence by it's framing of Trump against an embedded Deep State of pedophiles and Satan-worshipers. I am not sure where the conspiracy theory will go once Trump is gone. Will it die out, or has Trumpism irreversibly changed the GOP which will allow QAnon or something like it to remain a powerful social force moving forward? Social media memes like the attached picture are in my opinion indicative of a political movement that has no guarantee of dying out following Trump's departure from office.